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数学进展 - 2016, Vol. 45(1): 1-20
综述文章
图的划分: 一些进展与未解决问题
Graph Partitions: Recent Progresses and Some Open Problems

许宝刚
XU Baogang

南京师范大学数学科学学院数学研究所, 南京, 江苏, 210023
Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu, 210023, P. R. China

收稿日期: 2015-01-04
2016, Vol. 45(1): 1-20
DOI: 10.11845/sxjz.2015001a


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摘要 图的划分问题是图论研究中最重要的一个问题之一, 图论研究的很多问题都是特殊形式的划分问题, 比如经典染色理论要求将图划分成最少的独立集, 而最大 k-部子图问题则是要找图中边数最多的一个 k-部子图. 本文给出划分问题的一些最新进展, 以及一些尚未解决的问题, 其中大部分是来自于求最大k-部子图的相关领域.
Abstract:Graph partition problem is one of the most important topics in structural graph theory, since many problems in graph theory can be treated as a partition of the vertices into sets with some properties. For instance, the classical vertex coloring problem asks for a partition into minimum number of independent sets, and the maximum k-partite subgraph problem asks for a k-partite subgraph with maximum number of edges. In this paper, we present some results and problems on graph partitions, of which most are from the topic originated from the maximum k-partite subgraph problem.
PACS:  O157.5  
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